Chapter 2.6, Problem 96E

Archaeology: carbon $\text{-}14$ dating. The radioactive carbon $\text{-}14\left({}^{14}\text{C}\right)$ in an organism at the time of its death decays according to the equation

$A=A_0{e}^{-0.000124t}$

where $t$ is time in years and $A_0$ is the amount of ${}^{14}\text{C}$ present at time $t=0$. (See Example $3$ in Section $2.5$.) Estimate the age of a skull uncovered in an archaeological site if $10\%$ of the original amount of ${}^{14}\text{C}$ is still present. [Hint: Find $t$ such that $A=0.1A_0$ ]